6 #include "isl_map_private.h"
7 #include "isl_equalities.h"
8 #include "isl_sample.h"
10 struct isl_basic_map *isl_basic_map_implicit_equalities(
11 struct isl_basic_map *bmap)
22 if (F_ISSET(bmap, ISL_BASIC_MAP_EMPTY))
24 if (F_ISSET(bmap, ISL_BASIC_MAP_NO_IMPLICIT))
28 rational = F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL);
30 isl_int_init(opt_denom);
32 isl_int_set_si(opt_denom, 1);
33 for (i = 0; i < bmap->n_ineq; ++i) {
34 enum isl_lp_result res;
35 res = isl_solve_lp(bmap, 1, bmap->ineq[i]+1, ctx->one,
36 &opt, rational ? &opt_denom : NULL);
37 if (res == isl_lp_unbounded)
39 if (res == isl_lp_error)
41 if (res == isl_lp_empty) {
42 bmap = isl_basic_map_set_to_empty(bmap);
45 if (!isl_int_is_one(opt_denom))
47 isl_int_add(opt, opt, bmap->ineq[i][0]);
48 if (isl_int_is_zero(opt)) {
49 isl_basic_map_inequality_to_equality(bmap, i);
53 isl_int_clear(opt_denom);
56 F_SET(bmap, ISL_BASIC_MAP_NO_IMPLICIT);
60 isl_basic_map_free(bmap);
64 /* Make eq[row][col] of both bmaps equal so we can add the row
65 * add the column to the common matrix.
66 * Note that because of the echelon form, the columns of row row
67 * after column col are zero.
69 static void set_common_multiple(
70 struct isl_basic_set *bset1, struct isl_basic_set *bset2,
71 unsigned row, unsigned col)
75 if (isl_int_eq(bset1->eq[row][col], bset2->eq[row][col]))
80 isl_int_lcm(m, bset1->eq[row][col], bset2->eq[row][col]);
81 isl_int_divexact(c, m, bset1->eq[row][col]);
82 isl_seq_scale(bset1->eq[row], bset1->eq[row], c, col+1);
83 isl_int_divexact(c, m, bset2->eq[row][col]);
84 isl_seq_scale(bset2->eq[row], bset2->eq[row], c, col+1);
89 /* Delete a given equality, moving all the following equalities one up.
91 static void delete_row(struct isl_basic_set *bset, unsigned row)
98 for (r = row; r < bset->n_eq; ++r)
99 bset->eq[r] = bset->eq[r+1];
100 bset->eq[bset->n_eq] = t;
103 /* Make first row entries in column col of bset1 identical to
104 * those of bset2, using the fact that entry bset1->eq[row][col]=a
105 * is non-zero. Initially, these elements of bset1 are all zero.
106 * For each row i < row, we set
107 * A[i] = a * A[i] + B[i][col] * A[row]
110 * A[i][col] = B[i][col] = a * old(B[i][col])
112 static void construct_column(
113 struct isl_basic_set *bset1, struct isl_basic_set *bset2,
114 unsigned row, unsigned col)
123 total = 1 + isl_basic_set_n_dim(bset1);
124 for (r = 0; r < row; ++r) {
125 if (isl_int_is_zero(bset2->eq[r][col]))
127 isl_int_gcd(b, bset2->eq[r][col], bset1->eq[row][col]);
128 isl_int_divexact(a, bset1->eq[row][col], b);
129 isl_int_divexact(b, bset2->eq[r][col], b);
130 isl_seq_combine(bset1->eq[r], a, bset1->eq[r],
131 b, bset1->eq[row], total);
132 isl_seq_scale(bset2->eq[r], bset2->eq[r], a, total);
136 delete_row(bset1, row);
139 /* Make first row entries in column col of bset1 identical to
140 * those of bset2, using only these entries of the two matrices.
141 * Let t be the last row with different entries.
142 * For each row i < t, we set
143 * A[i] = (A[t][col]-B[t][col]) * A[i] + (B[i][col]-A[i][col) * A[t]
144 * B[i] = (A[t][col]-B[t][col]) * B[i] + (B[i][col]-A[i][col) * B[t]
146 * A[i][col] = B[i][col] = old(A[t][col]*B[i][col]-A[i][col]*B[t][col])
148 static int transform_column(
149 struct isl_basic_set *bset1, struct isl_basic_set *bset2,
150 unsigned row, unsigned col)
156 for (t = row-1; t >= 0; --t)
157 if (isl_int_ne(bset1->eq[t][col], bset2->eq[t][col]))
162 total = 1 + isl_basic_set_n_dim(bset1);
166 isl_int_sub(b, bset1->eq[t][col], bset2->eq[t][col]);
167 for (i = 0; i < t; ++i) {
168 isl_int_sub(a, bset2->eq[i][col], bset1->eq[i][col]);
169 isl_int_gcd(g, a, b);
170 isl_int_divexact(a, a, g);
171 isl_int_divexact(g, b, g);
172 isl_seq_combine(bset1->eq[i], g, bset1->eq[i], a, bset1->eq[t],
174 isl_seq_combine(bset2->eq[i], g, bset2->eq[i], a, bset2->eq[t],
180 delete_row(bset1, t);
181 delete_row(bset2, t);
185 /* The implementation is based on Section 5.2 of Michael Karr,
186 * "Affine Relationships Among Variables of a Program",
187 * except that the echelon form we use starts from the last column
188 * and that we are dealing with integer coefficients.
190 static struct isl_basic_set *affine_hull(
191 struct isl_basic_set *bset1, struct isl_basic_set *bset2)
197 total = 1 + isl_basic_set_n_dim(bset1);
200 for (col = total-1; col >= 0; --col) {
201 int is_zero1 = row >= bset1->n_eq ||
202 isl_int_is_zero(bset1->eq[row][col]);
203 int is_zero2 = row >= bset2->n_eq ||
204 isl_int_is_zero(bset2->eq[row][col]);
205 if (!is_zero1 && !is_zero2) {
206 set_common_multiple(bset1, bset2, row, col);
208 } else if (!is_zero1 && is_zero2) {
209 construct_column(bset1, bset2, row, col);
210 } else if (is_zero1 && !is_zero2) {
211 construct_column(bset2, bset1, row, col);
213 if (transform_column(bset1, bset2, row, col))
217 isl_basic_set_free(bset2);
218 isl_assert(ctx, row == bset1->n_eq, goto error);
221 isl_basic_set_free(bset1);
225 static struct isl_basic_set *isl_basic_set_from_vec(struct isl_ctx *ctx,
230 struct isl_basic_set *bset = NULL;
235 isl_assert(ctx, vec->size != 0, goto error);
237 bset = isl_basic_set_alloc(ctx, 0, vec->size - 1, 0, vec->size - 1, 0);
240 dim = isl_basic_set_n_dim(bset);
241 for (i = dim - 1; i >= 0; --i) {
242 k = isl_basic_set_alloc_equality(bset);
245 isl_seq_clr(bset->eq[k], 1 + dim);
246 isl_int_neg(bset->eq[k][0], vec->block.data[1 + i]);
247 isl_int_set(bset->eq[k][1 + i], vec->block.data[0]);
249 isl_vec_free(ctx, vec);
253 isl_basic_set_free(bset);
254 isl_vec_free(ctx, vec);
258 static struct isl_basic_set *outside_point(struct isl_ctx *ctx,
259 struct isl_basic_set *bset, isl_int *eq, int up)
261 struct isl_basic_set *slice = NULL;
262 struct isl_vec *sample;
263 struct isl_basic_set *point;
267 slice = isl_basic_set_copy(bset);
270 dim = isl_basic_set_n_dim(slice);
271 slice = isl_basic_set_extend(slice, 0, dim, 0, 1, 0);
272 k = isl_basic_set_alloc_equality(slice);
275 isl_seq_cpy(slice->eq[k], eq, 1 + dim);
277 isl_int_add_ui(slice->eq[k][0], slice->eq[k][0], 1);
279 isl_int_sub_ui(slice->eq[k][0], slice->eq[k][0], 1);
281 sample = isl_basic_set_sample(slice);
284 if (sample->size == 0) {
285 isl_vec_free(ctx, sample);
286 point = isl_basic_set_empty_like(bset);
288 point = isl_basic_set_from_vec(ctx, sample);
292 isl_basic_set_free(slice);
296 /* After computing the rational affine hull (by detecting the implicit
297 * equalities), we remove all equalities found so far, compute
298 * the integer affine hull of what is left, and then add the original
299 * equalities back in.
301 * The integer affine hull is constructed by successively looking
302 * a point that is affinely independent of the points found so far.
303 * In particular, for each equality satisfied by the points so far,
304 * we check if there is any point on the corresponding hyperplane
305 * shifted by one (in either direction).
307 struct isl_basic_map *isl_basic_map_affine_hull(struct isl_basic_map *bmap)
310 struct isl_mat *T2 = NULL;
311 struct isl_basic_set *bset = NULL;
312 struct isl_basic_set *hull = NULL;
313 struct isl_vec *sample;
317 bmap = isl_basic_map_implicit_equalities(bmap);
321 if (bmap->n_ineq == 0)
324 if (F_ISSET(bmap, ISL_BASIC_MAP_RATIONAL)) {
325 bmap = isl_basic_map_cow(bmap);
326 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
330 bset = isl_basic_map_underlying_set(isl_basic_map_copy(bmap));
331 bset = isl_basic_set_remove_equalities(bset, NULL, &T2);
333 sample = isl_basic_set_sample(isl_basic_set_copy(bset));
334 hull = isl_basic_set_from_vec(ctx, sample);
336 dim = isl_basic_set_n_dim(bset);
337 for (i = 0; i < dim; ++i) {
338 struct isl_basic_set *point;
339 for (j = 0; j < hull->n_eq; ++j) {
340 point = outside_point(ctx, bset, hull->eq[j], 1);
343 if (!F_ISSET(point, ISL_BASIC_SET_EMPTY))
345 isl_basic_set_free(point);
346 point = outside_point(ctx, bset, hull->eq[j], 0);
349 if (!F_ISSET(point, ISL_BASIC_SET_EMPTY))
351 isl_basic_set_free(point);
355 hull = affine_hull(hull, point);
358 isl_basic_set_free(bset);
360 bmap = isl_basic_map_cow(bmap);
363 isl_basic_map_free_inequality(bmap, bmap->n_ineq);
365 hull = isl_basic_set_preimage(ctx, hull, T2);
366 bmap = isl_basic_map_intersect(bmap,
367 isl_basic_map_overlying_set(hull,
368 isl_basic_map_copy(bmap)));
370 return isl_basic_map_finalize(bmap);
372 isl_mat_free(ctx, T2);
373 isl_basic_set_free(bset);
374 isl_basic_set_free(hull);
375 isl_basic_map_free(bmap);
379 struct isl_basic_set *isl_basic_set_affine_hull(struct isl_basic_set *bset)
381 return (struct isl_basic_set *)
382 isl_basic_map_affine_hull((struct isl_basic_map *)bset);
385 struct isl_basic_map *isl_map_affine_hull(struct isl_map *map)
388 struct isl_basic_map *model = NULL;
389 struct isl_basic_map *hull = NULL;
396 hull = isl_basic_map_empty_like_map(map);
401 map = isl_map_align_divs(map);
402 model = isl_basic_map_copy(map->p[0]);
403 set = isl_map_underlying_set(map);
404 set = isl_set_cow(set);
408 for (i = 0; i < set->n; ++i) {
409 set->p[i] = isl_basic_set_cow(set->p[i]);
410 set->p[i] = isl_basic_set_affine_hull(set->p[i]);
411 set->p[i] = isl_basic_set_gauss(set->p[i], NULL);
415 set = isl_set_remove_empty_parts(set);
417 hull = isl_basic_map_empty_like(model);
418 isl_basic_map_free(model);
420 struct isl_basic_set *bset;
422 set->p[0] = affine_hull(set->p[0], set->p[--set->n]);
426 bset = isl_basic_set_copy(set->p[0]);
427 hull = isl_basic_map_overlying_set(bset, model);
430 hull = isl_basic_map_simplify(hull);
431 return isl_basic_map_finalize(hull);
433 isl_basic_map_free(model);
438 struct isl_basic_set *isl_set_affine_hull(struct isl_set *set)
440 return (struct isl_basic_set *)
441 isl_map_affine_hull((struct isl_map *)set);